Calculating SEM from measurements on more than one person

Whilst calculating the SEM from just one person is quite possible it assumes that the variability in measurements is the same for everyone. It is therefore generally advisable to make measurements on a number of different people to test this. In this example we’ve thus also made measurements on a second person (in blue, download Excel spreadsheet here).

As might be expected, the mean values of the two people are different. You can see that the magnitude of the deviations (vertical lines) are also different indicating that the measurements are less variable for person B who has a smaller standard deviation (2.1kg).

Given that we now have two different within subject standard deviations we need to decide how to combine these to give us an overall SEM. It is tempting to take the simple mean of the two measurements but statisticians suggest that a better measure is the root mean square average. In this case this works out to be 3.1 kg {=√((3.9² + 2.1²)/2)}.

In a spreadsheet it is probably simplest to do this by adding an additional row.

You can adjust the number of measurements by adjusting the number of columns or the number of people by adjusting the number of rows but otherwise this format can be used to calculate the SEM from any balanced repeatability study. (A balanced study is one in which the same number of repeat measurements is performed on all the people involved).